In this example, we are assuming that we have a collection of 2-dimensional independent data for which the 1-dimensional dependent data has some error component or is known to be noisy. The presence of noise implies that whatever surface this data represents does not necessarily pass through the given dependent data points. In this case, a surface is approximated by numerically smoothing the data using the lowess algorithm. For any given point to be plotted a window of close enough, surrounding data points will be used to compute a local, weighted, low order fit.

The new command ScatterPlot3D, from the Statistics package, provides a smoothed plot of the 2-D noisy data.

The independent data does not need to be regularly spaced, and is supplied as an n-by-3 Array or Matrix. Each of the n rows represents an individual point. The columns are the x-, y-, and z-values.

Here is an example. First, we'll look down upon the projection of the data points onto the x-y plane, and thus visualize the layout and spacing of the 2-D dependent data values.

In these examples, we are assuming that we have a collection of 2-dimensional independent data for which the 1-dimensional dependent data is accepted as correct. The goal is to produce a surface which must must pass through all of the data points. That is, at every x-y point of the independent data the height of the plotted surface must match the corresponding value of the dependent (z) data. In this case, a surface is computed numerically by interpolating the data.

New in Maple 16, it is now possible to produce an interpolated 3-D surface using both regular and irregularly spaced data.

Uniform data grid

In the case of a uniform 2-dimensional grid of data a surface plot can be generated using the surfdata command.

The data is comprised of a grid of x- and y-points. For the examples of this section, the data points are taken uniformly in each direction. The x-values are taken as as the integers from 1 to 7, and the y-values are taken as the integers from 1 to 9.

View of data points in the x-y plane

Here is a view of the input data points, which in this example is a full grid, uniformly spaced in both the x and y directions.

The first 3-D plot below is the piecewise-planar surface produced by default. The goal is to produce a smoother surface instead, and this will be accomplished by using the gridsize and interpolation options of the surfdata command.

The plotted surface is being overlaid here with both the 3-D point-plot as well as the (linear) patch-surface, so that the computed surface may be visually demonstrated to be authentic with respect to the original discrete data.

The following plot3d options control the general look of these plots, and are reused in this subsection. They are assigned to a single, reusable name so that the differences between methods is more clearly illustrated.

Note that the 3-D plot renderer does its own small amount smoothing of the surface. Hence, even when using the purely linear method of the computational interpolation scheme, the plot on the right below shows a modest level of surface smoothing.

With new functionality in Maple 16, it is now possible to create an interpolate 3-D surface from irregularly spaced data.

Here below is an example. The data is supplied as an n-by-3 Array or Matrix. Each row represents a point, which the columns interpreted as x-, y-, and z-value. First, we'll look down upon the projection of the data points onto the x-y plane and thus visualize the layout and spacing of the 2-D dependent data values.

This is the same data that was used for the ScatterPlot3D example in the Smoothing section. But in contrast to the smoothing example we are now supposing that the data points are to be interpolated, which is to say that the surface must pass directly through the data points.